I can't answer
for Beeper, but why would they be unnecessarily antagonistic to Apple? It's not related to their product or mission. Beeper offers interoperability. Antagonism is an undesired byproduct of any of this work, and it's immature to be antagonistic for no reason.
Will it be a cat-and-mouse game? Maybe. Will users stay? Probably. In many cases, Beeper users already WERE iMessage users. Beeper users ARE Discord users. They are users of the upstream service and explicitly want a unified and interoperable chat system, for one reason or another. Maybe it's more practicality than ideals, but it's all the same in the end.
That said, it's not like Beeper is new, and it doesn't seem like antagonism is a primary driver of operational issues yet, so it's not clear it's about to start any time soon, either. Perhaps one of the most annoying tech company strategies is to try to establish a horrid status quo before regulators and law enforcement have time to catch up with you, making it much harder to actually do anything about. I see Beeper as one of a small number of companies that are basically on the opposite end; if they gain a large enough mass of users, it's going to be harder and harder to antagonize Beeper without antagonizing their own userbase, especially when you consider that the value of IM networks is largely in the connections between users. So, the clock is ticking.